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Names and Quantifiers: Bringing Them Together in Classical Logic
Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences:...
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Relational Syllogisms with Numerical Quantifiers and Beyond
In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set...
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Chapter 11 Categories of First-Order Quantifiers
One well known problem regarding quantifiers, in particular the 1st-order quantifiers, is connected with their syntactic categories and denotations....
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An Axiom System for Basic Hybrid Logic with Propositional Quantifiers
We present an axiom system for basic hybrid logic extended with propositional quantifiers (a second-order extension of basic hybrid logic) and prove...
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Grounding, Quantifiers, and Paradoxes
The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or...
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Definitional Quantifiers Realise Semantic Reasoning for Proof by Induction
Proof assistants offer tactics to apply proof by induction, but these tactics rely on inputs given by human engineers. To automate this laborious...
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Quantifier variance, semantic collapse, and “genuine” quantifiers
Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a...
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Generalized Quantifiers Meet Modal Neighborhood Semantics
In a mathematical perspective, neighborhood models for modal logic are generalized quantifiers, parametrized to points in the domain of...
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A Cook’s Tour of Duality in Logic: From Quantifiers, Through Vietoris, to Measures
We identify and highlight certain landmark results in Samson Abramsky’s work which we believe are fundamental to current developments and future...
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Fuzzy Generalised Quantifiers for Natural Language in Categorical Compositional Distributional Semantics
Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised...
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Carnap’s Problem, Definability and Compositionality
In his Formalization of Logic (1943) Carnap pointed out that there are non-normal interpretations of classical logic: non-standard interpretations of...
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Are generics quantificational?
The standard view about generic generalizations is that they have a tripartite quantificational logical form involving a phonologically null...
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Composition as Identity, Universalism, and Generic Quantifiers
Composition as Identity (CAI) is, roughly, the thesis that the parts of a whole, taken collectively, are in some sense identical with the whole....
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Quantifying Over Indiscernibles
One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over...
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Convexity and Monotonicity in Language Coordination: Simulating the Emergence of Semantic Universals in Populations of Cognitive Agents
Natural languages vary in their quantity expressions, but the variation seems to be constrained by general properties, so-called universals . Their...
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Quantification in the interpretational theory of validity
According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with...
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Identity and Quantification
This work examines a number of arguments to the effect that quantification requires identity of the objects that are quantified over; the arguments...
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The problem of mixed beings
According to ontological pluralism there are several ways of being. This is so if there is an unrestricted quantifier (∃ u ) that ranges over...
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First-Order Modal Tableaus
In Sects. 7.1 and 7.2 we gave prefixed tableau...
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Vague connectives
Most literature on vagueness deals with the phenomenon as applied to predicates. On the contrary, even the idea of vague connectives seems to be...
